Answer:
![v=(6ti+6k)\ m/s](https://tex.z-dn.net/?f=v%3D%286ti%2B6k%29%5C%20m%2Fs)
Explanation:
Given that,
The position of a particle is given by :
![r(t) = (3.0 t^2 i + 5.0j+ 6.0 tk) m](https://tex.z-dn.net/?f=r%28t%29%20%3D%20%283.0%20t%5E2%20i%20%2B%205.0j%2B%206.0%20tk%29%20m)
Let us assume we need to find its velocity.
We know that,
![v=\dfrac{dr}{dt}\\\\=\dfrac{d}{dt}(3.0 t^2 i + 5.0j+ 6.0 tk) \\\\=(6ti+6k)\ m/s](https://tex.z-dn.net/?f=v%3D%5Cdfrac%7Bdr%7D%7Bdt%7D%5C%5C%5C%5C%3D%5Cdfrac%7Bd%7D%7Bdt%7D%283.0%20t%5E2%20i%20%2B%205.0j%2B%206.0%20tk%29%20%5C%5C%5C%5C%3D%286ti%2B6k%29%5C%20m%2Fs)
So, the velocity of the particle is
.
Answer:
so its easier to understand for the reader
Explanation:
To solve this problem we will apply the concept of wavelength, which warns that this is equivalent to the relationship between the speed of the air (in this case in through the air) and the frequency of that wave. The air is in standard conditions so we have the relation,
Frequency ![= f = 562Hz](https://tex.z-dn.net/?f=%3D%20f%20%3D%20562Hz)
Speed of sound in air ![= v = 331m/s](https://tex.z-dn.net/?f=%3D%20v%20%3D%20331m%2Fs)
The definition of wavelength is,
![\lambda = \frac{v}{f}](https://tex.z-dn.net/?f=%5Clambda%20%3D%20%5Cfrac%7Bv%7D%7Bf%7D)
Here,
v = Velocity
f = Frequency
Replacing,
![\lambda = \frac{331m/s}{562Hz}](https://tex.z-dn.net/?f=%5Clambda%20%3D%20%5Cfrac%7B331m%2Fs%7D%7B562Hz%7D)
![\lambda = 0.589m](https://tex.z-dn.net/?f=%5Clambda%20%3D%200.589m)
Therefore the wavelength of that tone in air at standard conditions is 0.589m
The force acting on the object is constant, so the acceleration of the object is also constant. By definition of average acceleration, this acceleration was
<em>a</em> = ∆<em>v</em> / ∆<em>t</em> = (6 m/s - 0) / (1.7 s) ≈ 3.52941 m/s²
By Newton's second law, the magnitude of the force <em>F</em> is proportional to the acceleration <em>a</em> according to
<em>F</em> = <em>m a</em>
where <em>m</em> is the object's mass. Solving for <em>m</em> gives
<em>m</em> = <em>F</em> / <em>a</em> = (10 N) / (3.52941 m/s²) ≈ 2.8 kg